2 Game theory and network effects Your former roommate created a Business to

# 2 game theory and network effects your former

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2. (Game theory and network effects) Your former roommate created a Business-to-Business (B2B) Internet venture directed at an industry with exactly 50 identical firms, and hires you to assist with pricing. Using this service allows these firms to do business more efficiently as members of the trading network. You plan to sell access to your network for a price P per member firm. Each firm’s benefit from the service is 2 n , where n is the number of other members in the network. So, if 21 firms join, each member has a benefit of 2×20=\$40. Task 1: Suppose firms choose simultaneously and independently whether to join (that is, they choose whether or not to join without observing the decision of other firms first). Show that if P = \$2, there are two Nash equilibria of this game. What are the payoffs to the member firms in each equilibrium? What if P = \$50? And what if P = \$95?